The spread was small, with 40 percent favoring Cheney, and 15 percent with no opinion in a survey with a margin of error of 4 points.
"This may be the most important vice presidential debate in modern history," says Timothy Walch, director of the Herbert Hoover Presidential Library and Museum. "More people will tune in because last week's debate created a buzz of publicity."
Widespread consensus was Sen. John Kerry outperformed President George Bush at their first debate, held in Miami.
Aides said Edwards, a criminal lawyer, will try to follow Kerry's example from last week's debate with Bush by drawing stark differences with the administration's policy in Iraq and on key domestic issues.
On the other side, Cheney "won't be fancy or funny or gimmicky," said campaign adviser Mary Matalin. Cheney's goal will be to show "why these first post-Cold War, post-Sept. 11 policies will make us safer."